The key to the weak-ties phenomenon

TL;DR

The paper addresses why weak ties emerge in social networks and how mutual friends and tie weights influence future connections. It introduces three local link-prediction scores that incorporate direct edge weights and common neighbors with an exponent α: $S_{ij}^{DWCN}=\sum_{k\in\Gamma(i,j)} \omega(i,j)^\alpha$, $S_{ij}^{CN}=|\Gamma(i,j)|$, $S_{ij}^{CNA}=\sum_{k\in\Gamma(i,j)} \omega(i,j)^\alpha+|\Gamma(i,j)|$, and $S_{ij}^{CND}=\omega(i,j)^\alpha$ (with $S_{ij}=0$ if $\omega(i,j)=0$). The authors evaluate evolving link-prediction accuracy $P_t$ on three networks (Facebook, Email, High-school) and demonstrate that for α<0, CNA and DWCN best capture the weak-ties effect, indicating elevated predictive power of low-weight ties when mutual neighbors contribute. They further validate robustness with a null model that randomizes weights (RW), showing that while CND loses significance under weight randomization, CNA and DWCN maintain performance, underscoring the causal role of mutual friends in weak-ties emergence. Overall, the work provides a data-driven, mechanism-focused account of weak ties and improves local prediction in large-scale social networks.

Abstract

The study of the weak-ties phenomenon has a long and well documented history, research into the application of this social phenomenon has recently attracted increasing attention. However, further exploration of the reasons behind the weak-ties phenomenon is still challenging. Fortunately, data-driven network science provides a novel way with substantial explanatory power to analyze the causal mechanism behind social phenomenon. Inspired by this perspective, we propose an approach to further explore the driving factors behind the temporal weak-ties phenomenon. We find that the obvious intuition underlying the weak-ties phenomenon is incorrect, and often large numbers of unknown mutual friends associated with these weak ties is one of the key reason for the emergence of the weak-ties phenomenon. In particular, for example scientific collaborators with weak ties prefer to be involved in direct collaboration rather than share ideas with mutual colleagues -- there is a natural tendency to collapse short strong chains of connection.

Figures (4)

• Figure 1: The network structure of the weak-ties phenomenon. In the field of social science, a tie indicates the relationship between two persons, a contact or friendship can be stated as a relationship. The number of contacts can be stated as the tie strength. Ties with fewer contacts are the so-called weak ties. In the field of network science, the link or edge is precisely the tie of social science, correspondingly, link weight is the direct analogue of tie strength. Links with lower weights are weak ties. Hence, the structure of these ties or links and the properties of the persons or nodes are our primary research focus. In this figure, the node size indicates the corresponding node degree, and the link width indicates its weight. Nodes $A$ and $B$ are connected by the weak tie --- a link with low weight, and nodes $C$ and $D$ are connected by the link which has higher weight. Based on the result of our previous study Shang2017, the pair of nodes $A$ and $B$ associated with the weak tie will have more common neighbors --- the nodes connected by nodes $A$ and $B$ at the same time, then have a higher probability of receiving a relationship between them in the future.
• Figure 2: First, we can freely choose two links that have unequal weights, in this example the weights of $AB$ are 3, and the weights of $CD$ are 2. Then we exchange the weights of the two links. Here, after the randomization, the weight of $AB$ is 2, the weight of $CD$ is 3.
• Figure 3: The variation with link weight exponent $\alpha$ of the prediction accuracy $P_t$ of three link prediction algorithms, $DWCN$, $CNA$ and $CND$, applied to four different networks. Each value of $P_t$ plotted is the mean over $100$ independent trials.
• Figure 4: After the randomization of link weights, the prediction accuracy of $DWCN$ and $CNA$ with the variation of $\alpha$ by the measure of $P_t$ for Email and Contact networks.